Encryption using stirling matrices

This thesis examines Stirling numbers in detail and presents their general properties. Furthermore, the general applications of these numbers are examined and an application is given. The thesis's chapters are as follows. The first chapter covers the historical development of Stirling numbers and their literature. Stirling numbers and the Pascal matrix are examined in detail, and Stirling matrices are defined, for use throughout the thesis. The second chapter examines Fibonacci polynomials and introduces Stirling polynomials of the first and second types. The third chapter provides basic information about cryptography, supported by clear algorithms. Some essential algebraic concepts are introduced. The existence of finite fields and their place in cryptology are examined. Field extensions and operations are discussed. AES-type encryption, which has been used in many studies, is also examined. The final chapter of the thesis generalizes the Stirling polynomials presented in the second chapter. Irreducible Stirling polynomials are presented. An example of AES-type encryption using Stirling polynomials is presented.